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arXiv · 2404.09025

Maximal tori in infinite-dimensional Hamiltonian systems: a Renormalization Group approach

Livia Corsi·Guido Gentile·Michela Procesi
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Abstract

We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each other. We consider explicitly interactions depending only on the angles, with the aim of discussing in a simple case the analyticity properties to be required on the perturbation of the integrable system in order to ensure the persistence of a large measure set of invariant tori with finite energy. The proof we provide of the persistence of the invariant tori implements the Renormalization Group scheme based on the tree formalism -- i.e. the graphical representation of the solutions of the equations of motion in terms of trees -- which has been widely used in finite-dimensional problems. The method is very effectual and flexible: it naturally extends, once the functional setting has been fixed, to the infinite-dimensional case with only minor technical-natured adaptations.

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Livia Corsi, Guido Gentile, Michela Procesi. 2024-04-13. Maximal tori in infinite-dimensional Hamiltonian systems: a Renormalization Group approach. https://arxiv.org/abs/2404.09025

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